ci.bscor: Confidence interval for a biserial correlation
Description
Computes a confidence interval for a population biserial correlation. A
biserial correlation can be used when one variable is quantitative and the
other variable has been artificially dichotomized to create two groups.
The biserial correlation estimates the correlation between the observed
quantitative variable and the unobserved quantitative variable that has
been measured on a dichotomous scale.
Usage
ci.bscor(alpha, m1, m2, sd1, sd2, n1, n2)
Value
Returns a 1-row matrix. The columns are:
Estimate - estimated biserial correlation
SE - standard error
LL - lower limit of the confidence interval
UL - upper limit of the confidence interval
Arguments
alpha
alpha level for 1-alpha confidence
m1
estimated mean for group 1
m2
estimated mean for group 2
sd1
estimated standard deviation for group 1
sd2
estimated standard deviation for group 2
n1
sample size for group 1
n2
sample size for group 2
Details
This function computes a point-biserial correlation and its standard error
as a function of a standardized mean difference with a weighted variance
standardizer. Then the point-biserial estimate is transformed into a
biserial correlation using the traditional adjustment. The adjustment is
also applied to the point-biserial standard error to obtain the standard
error for the biserial correlation.
The biserial correlation assumes that the observed quantitative variable
and the unobserved quantitative variable have a bivariate normal
distribution. Bivariate normality is a crucial assumption underlying the
transformation of a point-biserial correlation to a biserial correlation.
Bivariate normality also implies equal variances of the observed
quantitative variable at each level of the dichotomized variable, and this
assumption is made in the computation of the standard error.